S S symmetry Article Gravitating Bubbles of Gluon Plasma above Deconfinement Temperature Yves Brihaye 1 and Fabien Buisseret 2,3,∗ 1 Service de Physique de l’Univers, Champs et Gravitation, UMONS Research Institute for Complex Systems, Université de Mons, Place du Parc 20, 7000 Mons, Belgium;
[email protected] 2 Service de Physique Nucléaire et Subnucléaire, UMONS Research Institute for Complex Systems, Université de Mons, Place du Parc 20, 7000 Mons, Belgium 3 CeREF, Chaussée de Binche 159, 7000 Mons, Belgium * Correspondence:
[email protected] Received: 2 September 2020; Accepted: 8 October 2020; Published: 13 October 2020 Abstract: The equation of state of SU(3) Yang–Mills theory can be modelled by an effective Z3−symmetric potential depending on the temperature and on a complex scalar field f. Allowing f to be dynamical opens the way to the study of spatially localized classical configurations of the scalar field. We first show that spherically symmetric static Q-balls exist in the range (1 − 1.21) × Tc, Tc being the deconfinement temperature. Then we argue that Q-holes solutions, if any, are unphysical within our framework. Finally, we couple our matter Lagrangian to Einstein gravity and show that spherically symmetric static boson stars exist in the same range of temperature. The Q-ball and boson-star solutions we find can be interpreted as “bubbles” of deconfined gluonic matter; their mean radius is always smaller than 10 fm. Keywords: deconfinement; Matter-gravity coupling; Yang–Mills theory; Q-ball; boson star 1. Introduction A fascinating feature of Yang–Mills theory is the existence of a deconfinement temperature, Tc, above which free color charges (free gluons) may propagate without being confined into color singlets [1,2].